This achievement should occur naturally as you build up your zoo in Challenge mode. It states in the description that you can only earn this achievement in Challenge mode
Ways to give your zoo rating a boost:
Add new exhibits
Launch an advertising campaign
Complete challenges that specifically boost your zoo rating
I earned this achievement when I was Level 19 in my zoo. The game is pretty lenient in the sense that if your funds are low and you are waiting for more money to build more exhibits, your zoo rating will remain at its current level, rather than decrease. How long this last though I am not sure